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Contributions to abstract analytic number theory. (English) Zbl 1032.11041

The author describes some recent contributions to the theory of multiplicative arithmetic semigroups which have been initiated by John Knopfmacher. They concern weighted inversion theorems of the Wiener type, mean-value theorems for multiplicative functions, and Ramanujan expansions. Most of the results are presented without a proof, but combined with significant and interesting remarks.

MSC:

11N80 Generalized primes and integers
11N37 Asymptotic results on arithmetic functions
11A25 Arithmetic functions; related numbers; inversion formulas
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